اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThree Easy Pieces (in tribute to Roman Jackiw)
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Frank Wilczek
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Roman Jackiw has made highly original and influential contributions to several areas of physics that have grown and blossomed, notably including the quantum physics of domain walls, magnetic monopoles, and fractional quantum numbers. Here I offer three small pieces that take off from those themes. I discuss the emergence of topological surface structure in materials, the emergence of a shape-space magnetic monopole in a simple mechanical system, and the emergence of fractional angular momentum in an even simpler quantum mechanical (molecular) system.
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I recount my personal experience interacting with Roman Jackiw in the 1980s, when we both worked on Chern-Simons theories in three dimensions.
This text offers reminiscences of my personal interactions with Roman Jackiw as a way of looking back at the very fertile period in theoretical physics in the last quarter of the 20th century.
In this paper we analyze a generalized Jackiw-Rebbi (J-R) model in which a massive fermion is coupled to the kink of the $lambdaphi^4$ model as a prescribed background field. We solve this massive J-R model exactly and analytically and obtain the who
le spectrum of the fermion, including the bound and continuum states. The mass term of the fermion makes the potential of the decoupled second order Schrodinger-like equations asymmetric in a way that their asymptotic values at two spatial infinities are different. Therefore, we encounter the unusual problem in which two kinds of continuum states are possible for the fermion: reflecting and scattering states. We then show the energies of all the states as a function of the parameters of the kink, i.e. its value at spatial infinity ($theta_0$) and its slope at $x=0$ ($mu$). The graph of the energies as a function of $theta_0$, where the bound state energies and the two kinds of continuum states are depicted, shows peculiar features including an energy gap in the form of a triangle where no bound states exist. That is the zero mode exists only for $theta_0$ larger than a critical value $(theta_0^{textrm{c}})$. This is in sharp contrast to the usual (massless) J-R model where the zero mode and hence the fermion number $pm1/2$ for the ground state is ever present. This also makes the origin of the zero mode very clear: It is formed from the union of the two threshold bound states at $theta_0^{textrm{c}}$, which is zero in the massless J-R model.
In this work we focus on the Carroll-Field-Jackiw (CFJ) modified electrodynamics in combination with a CPT-even Lorentz-violating contribution. We add a photon mass term to the Lagrange density and study the question whether this contribution can ren
der the theory unitary. The analysis is based on the pole structure of the modified photon propagator as well as the validity of the optical theorem. We find, indeed, that the massive CFJ-type modification is unitary at tree-level. This result provides a further example for how a photon mass can mitigate malign behaviors.
In this note we study the $1+1$ dimensional Jackiw-Teitelboim gravity in Lorentzian signature, explicitly constructing the gauge-invariant classical phase space and the quantum Hilbert space and Hamiltonian. We also semiclassically compute the Hartle
-Hawking wave function in two different bases of this Hilbert space. We then use these results to illustrate the gravitational version of the factorization problem of AdS/CFT: the Hilbert space of the two-boundary system tensor-factorizes on the CFT side, which appears to be in tension with the existence of gauge constraints in the bulk. In this model the tension is acute: we argue that JT gravity is a sensible quantum theory, based on a well-defined Lorentzian bulk path integral, which has no CFT dual. In bulk language, it has wormholes but it does not have black hole microstates. It does however give some hint as to what could be added to to rectify these issues, and we give an example of how this works using the SYK model. Finally we suggest that similar comments should apply to pure Einstein gravity in $2+1$ dimensions, which wed then conclude also cannot have a CFT dual, consistent with the results of Maloney and Witten.
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